有限非链环Fpm+vFpm上循环码的迹码和子环子码

doi:10.3969/j.issn.0372-2112.2019.01.032

PDF(444 KB)

电子学报 ›› 2019, Vol. 47 ›› Issue (1) : 241-244. DOI: 10.3969/j.issn.0372-2112.2019.01.032

科研通信

有限非链环F_p^m+vF_p^m上循环码的迹码和子环子码

高健, 李娟

作者信息 +

On Trace Codes and Subring Subcodes of Cyclic Codes Over Finite Non-Chain Ring F_p^m+vF_p^m

GAO Jian, LI Juan

Author information +

文章历史 +

摘要

给出了有限非链环F_p^m+vF_p^m的Galois扩环相关理论，明确了有限非链环F_p^m+vF_p^m上循环码的迹码和子环子码的生成元结构.

Abstract

In this paper,we give some results on the Galois extension of the finite non-chain ring F_p^m+vF_p^m. We also determine the generators of trace codes and subring subcodes of cyclic codes over the finite non-chain ring F_p^m+vF_p^m.

导出引用

高健, 李娟. 有限非链环F_p^m+vF_p^m上循环码的迹码和子环子码[J]. 电子学报, 2019, 47(1): 241-244. https://doi.org/10.3969/j.issn.0372-2112.2019.01.032

GAO Jian, LI Juan. On Trace Codes and Subring Subcodes of Cyclic Codes Over Finite Non-Chain Ring F_p^m+vF_p^m[J]. Acta Electronica Sinica, 2019, 47(1): 241-244. https://doi.org/10.3969/j.issn.0372-2112.2019.01.032

中图分类号： TN911.22

参考文献

[1] HAMMONS A,KUMAR P,CALDERBANK A,et al.The Z₄-linearity of Kerdock,Preparata,Goethals,and related codes[J].IEEE Transactions on Information Theory,1994,40(2):301-319.
[2] 吴波,朱世信,李平.环F_p+uF_p上的Kerdock码和Preparata码[J].电子学报,2008,36(7):1364-1367. WU Bo,ZHU Shi-xin,LI Ping.Kerdock code and Preparata code over ring F_p+uF_p[J].Acta Electronica Sinica,2008,36(7):1364-1367.(in Chinese)
[3] 施敏加,刘艳.环F_p+vF_p+v²F_p上线性码的各种重量计数器及其MacWilliams恒等式[J].电子学报,2014,42(7):1387-1391. SHI Min-jia,LIU Yan.Several weight enumerators of linear codes and their MacWilliams identities over ring F_p+vF_p+v²F_p[J].Acta Electronica Sinica,2014,42(7):1387-1391.(in Chinese)
[4] GAO J.Some results on linear codes over F_p+uF_p+u²F_p[J].Journal of Applied Mathematics and Computing,2015,47(1):473-485.
[5] 张光辉.环F_p+vF_p上线性码的极小支座谱[J].电子学报,2015,43(8):1621-1626. ZHANG Guang-hui.On the minimum support hierarchy of linear codes over F_p+vF_p[J].Acta Electronica Sinica,2015,43(8):1621-1626.(in Chinese)
[6] ZHU S,WANG Y,SHI M.Some results on cyclic codes over F₂+vF₂[J].IEEE Transations on Information Theory,2010,56(4):1680-1684.
[7] DELSARTE P.On subfield subcodes of modified Reed-Solomon codes[J].IEEE Transations on Information Theory,1975,21(5):575-576.
[8] 朱士信,黄磊.环R+vR+v²R上线性码的MacWilliams恒等式[J].电子学报,2016,44(7):1567-1573. ZHU S-X,HUANG L.Mac Williams identities of linear codes over ring R+vR+v²R[J].Acta Electronica Sinica,2016,44(7):1567-1573.(in Chinese)
[9] WANG L,WANG Z,HUANG Q,et al.Balanced gray codes with flexible lengths[J].IEEE Communications Letters,2016,20(5):894-897.
[10] 宋云,李志慧,李永明.基于极小线性码上的秘密共享方案[J].电子学报,2013,41(2):220-226. SONG Y,LI Z-H,LI Y-M.Secret sharing schemes on minimal linear codes[J].Acta Electronica Sinica,2013,41(2):220-226.(in Chinese)
[11] GAO Z,FU F-W.Linear recurring sequences and subfied subcodes of cyclic codes[J].Science China Mathematics,2013,56(7):1413-1420.
[12] MARTÍNEZ-MORO E,NICOLÍS A P,RUA I F.On trace codes and Galois invariance over finite commutative chain rings[J].Finite Fields and Their Applications,2013,22:114-121.